The purpose of this project is to develop new compression techniques and to study their efficiency for the coding of cervical and lumbar spine x-ray data. We have chosen to concentrate our efforts on multiresolution schemes, which are especially suited for progressive transmission. Our present approach uses a pyramidal image representation that consists of a series of increasingly coarser copies of the original, with a scale reduction by a factor of two at each step. The quantized differences between successive levels in this pyramid are then coded for transmission. The image is reconstructed in a progressive fashion, starting from its coarsest representation. Our contribution has been in the design of an improved reduction algorithm based on the principle of least squares approximation. This approach is, in fact, closely related to the wavelet transform.